Question: Simplify. Rewrite the expression in the form $10^n$. $10^5\cdot 10=$
$\begin{aligned} 10^5\cdot 10&=10^5\cdot 10^1 \\\\ &=10^{5+1} \\\\ &=10^{6} \end{aligned}$ This follows from the general rule $x^m\cdot x^n=x^{m+n}$. Note that the powers have the same base. We can also see this is correct by expanding the powers. $\begin{aligned} 10^5\cdot 10&=\underbrace{10\cdot 10\cdot 10\cdot 10\cdot 10}_\text{5 times}\cdot\underbrace{10}_\text{1 time} \\\\\\ &=\underbrace{10\cdot 10\cdot 10\cdot 10\cdot 10\cdot 10}_\text{6 times} \\\\ &=10^{6} \end{aligned}$ In conclusion, $10^5\cdot 10=10^{6}$.